
// Make newform 6034.2.a.n in Magma, downloaded from the LMFDB on 20 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_6034_a();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_6034_2_a_n();".
// This may take a long time!  To see verbose output, uncomment the SetVerbose line below.
// The default sign is -1.  You can change this with the optional parameter "sign".
// To make the character of type GrpDrchElt, type "MakeCharacter_6034_a();"
function MakeCharacter_6034_a()
    N := 6034;
    order := 1;
    char_gens := [1725, 869];
    v := [1, 1];
    // chi(gens[i]) = zeta^v[i]
    assert UnitGenerators(DirichletGroup(N)) eq char_gens;
    F := CyclotomicField(order);
    chi := DirichletCharacterFromValuesOnUnitGenerators(DirichletGroup(N,F),[F|F.1^e:e in v]);
    return MinimalBaseRingCharacter(chi);
end function;

function MakeCharacter_6034_a_Hecke(Kf)
    return MakeCharacter_6034_a();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_6034_2_a_n();".
// This may take a long time!  To see verbose output, uncomment the SetVerbose line below.
// The default sign is -1.  You can change this with the optional parameter "sign".
function MakeNewformModSym_6034_2_a_n( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_6034_a();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<3,R![80, -2096, -28808, 170660, -113788, -632874, 858085, 793541, -1681181, -269671, 1567350, -223986, -810664, 255569, 244040, -110134, -41635, 25703, 3352, -3403, 15, 240, -21, -7, 1]>,<5,R![268111, -1249838, -1495527, 14351311, -14160664, -22999165, 38899132, 10157210, -40318071, 4521308, 21939954, -6441104, -6918166, 2890525, 1291246, -700432, -134746, 100717, 5672, -8597, 238, 403, -34, -8, 1]>,<11,R![-27387055, -988887866, -3046727520, 6970884742, 10487091732, -16890179464, -8770458486, 17409257237, 455954298, -7986381390, 1870007710, 1552557924, -647967957, -123236049, 94105512, -471668, -7053808, 755105, 270755, -51868, -4044, 1462, -28, -15, 1]>],Snew);
    return Vf;
end function;